MAYBE

Problem:
 p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))

Proof:
 DP Processor:
  DPs:
   p#(a(a(x0)),p(x1,p(a(x2),x3))) -> p#(a(a(x0)),x3)
   p#(a(a(x0)),p(x1,p(a(x2),x3))) -> p#(a(a(b(x1))),p(a(a(x0)),x3))
   p#(a(a(x0)),p(x1,p(a(x2),x3))) -> p#(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
  TRS:
   p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
  Restore Modifier:
   DPs:
    p#(a(a(x0)),p(x1,p(a(x2),x3))) -> p#(a(a(x0)),x3)
    p#(a(a(x0)),p(x1,p(a(x2),x3))) -> p#(a(a(b(x1))),p(a(a(x0)),x3))
    p#(a(a(x0)),p(x1,p(a(x2),x3))) -> p#(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
   TRS:
    p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 9/9
    DPs:
     p#(a(a(x0)),p(x1,p(a(x2),x3))) -> p#(a(a(x0)),x3)
     p#(a(a(x0)),p(x1,p(a(x2),x3))) -> p#(a(a(b(x1))),p(a(a(x0)),x3))
     p#(a(a(x0)),p(x1,p(a(x2),x3))) -> p#(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
    TRS:
     p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [p#](x0, x1) = x1,
      
      [b](x0) = 0,
      
      [p](x0, x1) = x1 + 1,
      
      [a](x0) = 1
     orientation:
      p#(a(a(x0)),p(x1,p(a(x2),x3))) = x3 + 2 >= x3 = p#(a(a(x0)),x3)
      
      p#(a(a(x0)),p(x1,p(a(x2),x3))) = x3 + 2 >= x3 + 1 = p#(a(a(b(x1))),p(a(a(x0)),x3))
      
      p#(a(a(x0)),p(x1,p(a(x2),x3))) = x3 + 2 >= x3 + 2 = p#(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
      
      p(a(a(x0)),p(x1,p(a(x2),x3))) = x3 + 3 >= x3 + 3 = p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
     problem:
      DPs:
       p#(a(a(x0)),p(x1,p(a(x2),x3))) -> p#(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
      TRS:
       p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
     Open